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Stabilized finite element methods. II: The incompressible Navier-Stokes equations. (English) Zbl 0765.76048
Summary: [For part I see, the authors and Th. J. R. Hughes, Rocquencourt: INRIA 1990, Rapp. Rech. 1300.]
Stabilized methods are proposed and analyzed for a linearized form of the incompressible Navier-Stokes equations. The methods are extended and tested for the nonlinear model. The methods combine the good features of stabilized methods already proposed for the Stokes flow and for advective-diffusive flows. These methods also generalize previous works restricted to low-order interpolations, thus allowing any combination of velocity and continuous pressure interpolations. A careful design of the stability parameters is suggested which considerably simplifies these generalizations.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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